The Daily Mail demeaned the political process with its attack on Ralph Miliband, the former deputy prime minister Lord Heseltine has said.

In remarks that went further than the careful response of Tory ministers, Heseltine said there was no justification for the headline on the Miliband piece which said he hated Britain.

Heseltine told The Daily Politics on BBC2: "This is carrying politics to an extent that is just demeaning, frankly. The headline isn't justified. It is completely out of context. As everybody knows the guy fought for this country and we now live in a totally different world to the clash between communism and fascism."

The former deputy prime minister addressed the Mail's claim that Marxists such as Ralph Miliband deserved to be condemned because of the repression of the Soviet Union. He said: "Let us be frank. Stalin did some of the most appalling things but the Russians turned the second world war."

Heseltine also said the Mail had published "hatchet jobs" on Ed Miliband and Nick Clegg.

William Hague had earlier said the Mail's attack has no implications for the future regulation of the press in Britain. The foreign secretary said it was understandable that the Labour leader had decided to defend his father after the Mail said that Ralph Miliband's Marxist writings showed he hated Britain.

Hague declined to say whether the newspaper had carried out a hatchet job as he said: "These things do happen."

Many ministers believe in private that the Mail made a serious error in saying that Ralph Miliband, who fought for Britain in the second world war after escaping the Holocaust, hated the country. But they are declining to criticise the Mail because they do not want to fuel the row, which has overshadowed the past 48 hours of the Conservative conference, ahead of negotiations over the future of press regulation.

But a member of the prime minister's No 10 policy board criticised the Mail. Margot James, MP for Stourbridge, tweeted: "Crass and cruel to condemn Ralph M'band for his Marxist views when they were formed in 40/50s, deeply misguided maybe but not unpatriotic."

Hague simply supported Ed Miliband's decision to defend his father, though he acknowledged that the Daily Mail's deputy editor, John Steafel, had said the paper that Mail Online had been wrong to run a picture of Ralph Miliband's gravestone with the words "grave socialist".

The foreign secretary told the Today programme on BBC Radio 4: "I think it is very understandable that a son in any walk of life, not just a politician, comes to the defence of a parent. That is what we would expect to happen and that is clearly what is happening here. We should understand and respect that. I am in no position to judge myself about it and he will have known his father far better than any of us could have possibly have done."

Asked whether the Mail had carried out a hatchet job on Ralph Miliband, Hague said: "I am going to leave that for the leader of the opposition and the Daily Mail to argue about. I notice that they have said it was an error of judgment to use a picture of the grave in the way that they did. But I think that is best left to them.

"I don't think we can jump to wider conclusions about the regulation of the press or the wider political argument. These things do happen – arguments between politicians – and I know them well. It is understandable that someone comes to the defence of their parents."

The London mayor, Boris Johnson, told LBC 97.3 he understood Ed Miliband's reaction. "What I actually feel, I've got ancestry that doesn't come from this country and I think people do feel very sensitive, particularly if the patriotism of those relatives is impugned," he said.

"I can imagine that being a very, very hurtful thing and I would definitely want to fire back if it was me."

Charles Moore, the former editor of the Daily Telegraph, accused the Daily Mail of offending against taste and decency on "multiple fronts".

Moore, who is the official biographer, writes in this week's Spectator magazine: "The Mail managed to offend against taste and decency on multiple counts – attacking a man for his deceased father's views, misrepresenting those views, attacking a Jew, attacking a refugee from Hitler."

The Daily Mail should simply have focused on Ralph Miliband's Marxist views – and his son's move to the left. It should not have accused Ralph Miliband of hating Britain, Moore said. He wrote: "Why did it not stick to the red angle? Although it is true that a significant minority on the left was actually treacherous in its support for the Soviet Union, even more harm was done by honest, decent patriots, such as Ralph Miliband, who thought that state socialism was the answer to our woes.

"People are so anti-Tony Blair these days that they have forgotten how heroically he squashed such views and thus made his party electable. Young Miliband took a giant step backward last week. That is the point that needs making all the time.

Downing Street is working hard to ensure that ministers keep out of the Labour row with the Mail. Ministers have been told to make a simple argument that any child would rightly want to defend a parent.

David Cameron said in his interview on the Today programme on Tuesday, which took place at 8.10am, that he had not read the Daily Mail piece. He said the same thing three hours later in separate interviews with the main television news programmes. By early afternoon, by which time he would be facing no more interviews until after the conference, Tory sources let it be known that the prime minister had read the Mail article.

The Guardian has published an extensive critique of the Daily Mail and its reporting of Labour, press regulation and the Snowden leaks. We invited Mail readers to join in that debate. Paul Dacre, editor-in-chief, asked for the opportunity to comment. Here is his contribution